A cosmologically viable eV sterile neutrino model

C. A. de S. Pires

REVIEW 3 major objections 5 minor 27 references

A cosmologically viable eV sterile neutrino model

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read This paper claims that the canonical type I seesaw, run at eV-to-keV VEVs with a sub-eV pseudo-scalar coupled only to sterile neutrinos, can generate the eV sterile neutrino hinted by LSND and MiniBooNE while reconciling it with cosmology.

desk verdict A coherent model-building realization of the secret-interaction idea, but the only numerical benchmark is internally inconsistent and the cosmological claim is borrowed, not derived. read the letter →

arxiv 1908.09313 v1 pith:UXVHI2TZ submitted 2019-08-25 hep-ph

C. A. de S. Pires This is my paper · ORCID

classification hep-ph

keywords low-scaletypeIseesaweVsterileneutrinoLSNDanomalyMiniBooNEexcesssecretinteractionspseudo-scalarwarmdarkmattercosmology

topics Dark Matter

open problems Dark Matter

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper proposes an extension of the Standard Model in which the canonical type I seesaw mechanism operates at unusually low energy scales, with the second Higgs VEV around $10^2\,\mathrm{eV}$ and the singlet VEV around $10^5\,\mathrm{eV}$, generating tiny masses for both active and sterile neutrinos. This includes a fourth neutrino with mass around $1.4\,\mathrm{eV}$ and mixing with the active neutrinos in the range suggested by the LSND and MiniBooNE anomalies. To make that sterile neutrino cosmologically viable, the model contains a pseudo-scalar $I_\varphi$ that couples exclusively to sterile neutrinos and whose mass is pushed below $0.1\,\mathrm{eV}$ by choosing the explicit lepton-number-breaking scale $M$ below $10^{-8}\,\mathrm{eV}$. The author argues that the benchmark Yukawa coupling $Y_{S11}=2\times10^{-5}$ reproduces the secret interaction that, according to the cited literature, suppresses sterile-neutrino production in the early universe and reconciles eV sterile neutrinos with BBN, CMB, and large-scale structure. The model also yields a $7\,\mathrm{keV}$ sterile neutrino as long-lived warm dark matter, contributes to the muon $g-2$, and can host Higgs inflation.

What carries the argument

The load-bearing object is the pseudo-scalar $I_\varphi$, the imaginary part of the singlet field $\varphi$ that carries two units of lepton number; its mass is set by the trilinear term $\frac{M}{\sqrt{2}}(\varphi^3+\varphi^{*3})$, giving $M_{I_\varphi}^2=\frac{9}{4}M v_\varphi$. This field couples only to right-handed neutrinos through $\frac{i}{2}Y_S\,\overline{\nu_R^C}I_\varphi\nu_R$, realizing the secret interaction. The supporting machinery is a $\mathbb{Z}_3\times\mathbb{Z}_2$ symmetry plus two Higgs doublets and two singlet scalars, arranged so that neutrino masses arise only from the new scalars; with $v_2\sim100\,\mathrm{eV}$ and $v_\varphi\sim10^5\,\mathrm{eV}$, the seesaw formula produces the desired light sterile and active neutrino spectrum.

What would settle it

Compute the early-universe production of the sterile states in this model with $m_{I_\varphi}<0.1\,\mathrm{eV}$ and $Y_{S11}=2\times10^{-5}$; if the resulting effective number of extra neutrinos or the abundance of the $7\,\mathrm{keV}$ state exceeds the bounds from BBN, the cosmic microwave background, and large-scale structure, the central claim fails. A laboratory bound excluding a pseudo-scalar below $0.1\,\mathrm{eV}$ coupled to sterile neutrinos would also undercut it.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that the canonical type I seesaw does not need a GUT-scale right-handed neutrino: replacing the usual weak-scale VEV by $v_2\sim10^2\,\mathrm{eV}$ and taking the Majorana scale $v_\varphi\sim10^5\,\mathrm{eV}$ gives active neutrino masses of order $10^{-4}$ to $5\times10^{-2}\,\mathrm{eV}$, a sterile neutrino $\nu_4$ with mass $\sim1.4\,\mathrm{eV}$ and mixings $U_{e4}^2,\,U_{\mu4}^2\sim10^{-3}$-$10^{-2}$, and two heavier sterile states at $0.7\,\mathrm{keV}$ and $7\,\mathrm{keV}$. The same scalar content contains a pseudo-scalar $I_\varphi$ with mass squared $M_{I_\varphi}^2=\frac{9}{4}M v_\varphi$, which couples exclusively to sterile neutrinos. Choosing the explicit lepton-number-breaking scale $M<10^{-8}\,\mathrm{eV}$ puts $I_\varphi$ below $0.1\,\mathrm{eV}$, and with $Y_{S11}=2\times10^{-5}$ the coupling falls in the range that the cited secret-interaction mechanism claims suppresses sterile-neutrino thermalization. The benchmark spectrum recovers the 3+1 oscillation picture, with $\nu_5$ and $\nu_6$ effectively decoupled, and $\nu_6$ is a long-lived warm dark matter candidate.

Load-bearing premise

Everything hangs on the claim, taken from the earlier secret-interaction literature, that a pseudo-scalar lighter than $0.1\,\mathrm{eV}$ with a Yukawa coupling around $2\times10^{-5}$ to sterile neutrinos really stops them from being produced in the early universe; this paper does not calculate that suppression itself.

Editorial extensions

If this is right

If the model is correct, the LSND and MiniBooNE excess can be explained by a $1.4\,\mathrm{eV}$ sterile neutrino that evades cosmological bounds through the secret interaction.
The seesaw scale is not necessarily high: lepton number can be explicitly broken at $10^{-8}\,\mathrm{eV}$, and the right-handed Majorana scale can be as low as the keV range.
The model predicts a $7\,\mathrm{keV}$ sterile neutrino as warm dark matter, with a radiative decay lifetime around $10^{28}\,\mathrm{s}$, far longer than the age of the Universe.
The charged scalar of the model mediates $\mu\to e\gamma$, and the current bound forces $f v_\sigma \ge 36\times10^6\,\mathrm{GeV}^2$, a testable constraint on the scalar sector.
The singlet $\sigma$ can act as the inflaton in Higgs inflation with a non-minimal coupling $\xi<1$, avoiding the unitarity problem of minimal Higgs inflation.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The paper does not compute the sterile-neutrino production rate, $\Delta N_{\text{eff}}$, or the matter power spectrum in its own model; a direct calculation with $m_{I_\varphi}<0.1\,\mathrm{eV}$ and $Y_{S11}=2\times10^{-5}$ is the natural next step, and would test whether the heavier states $\nu_5$ and $\nu_6$ stay out of equilibrium.
The benchmark point is illustrative; a scan of the $Y_D$, $Y_S$, $v_2$, and $v_\varphi$ parameters would show how tuned the cosmological compatibility is and whether the mixing angles required by oscillation fits coexist with the chosen $Y_{S11}$.
If the secret-interaction mechanism works, a generic prediction is a sub-eV pseudo-scalar that interacts only with sterile neutrinos; improved measurements of $N_{\text{eff}}$ and searches for exotic decays involving sterile neutrinos could bound or confirm it.
The model's low-scale seesaw logic could be adapted to other neutrino-mass mechanisms, suggesting that eV sterile neutrinos do not require abandoning seesaw but rather rescaling its VEVs.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Dear colleague,

Here's my read of Pires' eV sterile neutrino model.

The genuinely new thing is a complete renormalizable model—two doublets, two singlets, right-handed neutrinos, Z3×Z2—that realizes the secret-interaction idea. Refs [11,12] proposed the mechanism but didn't embed it. The scalar sector is worked out in detail, and the CP-odd component Iφ does decouple and gets a mass M_Iφ^2 = (9/4) M vφ, so a sub-eV pseudo-scalar follows from a tiny M. That part is clean.

The soft spots are real. The illustrative benchmark in Eq. (13) doesn't produce the masses quoted in Eq. (14). Using their own seesaw formula with vD = 10 eV and vphi = 1e5 eV, the active mass matrix has eigenvalues of order 0.2, 0.03, and 0.002 eV, not 0.05, 0.0086, and 2e-4 eV. The solar and atmospheric match is therefore not demonstrated. The paper's only numerical example fails on the central phenomenological claim.

The cosmological side is also asserted rather than computed. The author assumes that YS11 = 2e-5 satisfies the g_s ~ 1e-5 window from Hannestad et al. and Dasgupta-Kopp. But the other two right-handed neutrinos couple to Iφ with YS22 = 0.01 and YS33 = 0.1, hundreds to thousands of times larger. If the secret interaction suppresses production only for g_s ~ 1e-5, the heavier states ν5 and ν6 could thermalize through the same interaction. The paper doesn't compute N_eff, BBN, or LSS constraints for the full model. That's a gap, not a fatal flaw, but it means the title's claim is not supported by the analysis.

Smaller things: the "lepton number violated at 10^-8 eV" headline is just the input condition m_Iφ < 0.1 eV recast; the muon g-2 and inflation sections are explicitly deferred; and the µ→eγ constraint uses the benchmark YDs without checking whether the resulting f vσ is compatible with the scalar spectrum.

Overall: the model-building idea is worth taking seriously, and the scalar-sector machinery is correct. But the paper as written doesn't back its two main claims—oscillation data and cosmological viability—with a valid numerical example or a computation. Both are fixable. I'd send it to a referee, but the referee should be told to focus on the benchmark and the thermalization of the heavy sterile states.

For a reading group, maybe, if someone in the group works on secret interactions. I wouldn't cite it in the next year until the benchmark is corrected.

Best

Referee Report

3 major / 5 minor

Summary. The paper proposes an extension of the Standard Model with three right-handed neutrinos, a second Higgs doublet H2, and two scalar singlets phi and sigma, subject to a Z3 x Z2 symmetry. The goal is to realize the type I seesaw mechanism at very low energy scales so that both active and sterile neutrinos are light, with an eV-mass fourth neutrino compatible with short-baseline anomalies, and to reconcile such an eV sterile neutrino with cosmology through a sub-eV pseudo-scalar Iphi that couples only to sterile neutrinos. The pseudo-scalar mass is derived as M_Iphi^2 = (9/4) M vphi, and the secret interaction is identified with the Yukawa term involving Iphi and the right-handed neutrinos, with a benchmark coupling YS11 = 2e-5. The paper also discusses constraints from mu -> e gamma and suggests that the scalar sigma could drive Higgs inflation.

Significance. If the benchmark and the cosmological argument were correct, the model would be a concrete realization of a low-scale type I seesaw with a 'secret interaction' pseudo-scalar, combining several phenomenological handles in one framework. A positive feature is the explicit derivation that Iphi decouples from the other CP-odd states and obtains a mass controlled by the lepton-number-violating parameter M. However, the only demonstrated benchmark for active neutrino masses is numerically inconsistent with the paper's own seesaw formula, and the cosmological viability is asserted rather than computed. These issues are central to the paper's claims, so the current version cannot be accepted as a demonstration of the proposed scenario.

major comments (3)

[II.B, Eqs. (13)-(14)] The illustrative benchmark does not reproduce the quoted active neutrino masses. With v2 = 10 eV, vphi = 10^5 eV and diagonal YS, Eq. (11) gives M_light = -(v2^2/(sqrt(2) vphi)) YD^T YS^{-1} YD. Substituting the values in Eq. (13), this 3x3 matrix has trace about 0.234 eV and eigenvalues approximately 0.20, 0.035 and 0.0007 eV, not the 0.05, 0.0086 and 0.0002 eV claimed in Eq. (14). Even the single 22 entry contributes about 0.12 eV before off-diagonal mixing, already exceeding the claimed m_nu3. The implied squared mass splittings are of order 1.2e-3 eV^2 and 3.8e-2 eV^2, which do not accommodate solar and atmospheric oscillations. The paper's own criterion is that one concrete benchmark suffices; this point does not satisfy that criterion, so a corrected and explicitly verified benchmark, including the full 6x6 diagonalization, is required.
[II.C] Cosmological viability is asserted rather than demonstrated. The reconciliation with BBN, CMB and LSS is based entirely on the claim in Refs. [11,12] that a sub-eV pseudo-scalar with g_s in the range 1e-6 to 1e-5 suppresses sterile-neutrino production; the present paper does not compute the production rate, N_eff, or structure-formation constraints in the model. Moreover, Eq. (20) couples Iphi to all three right-handed neutrinos with strengths YS11 = 2e-5, YS22 = 0.01 and YS33 = 0.1, so nu5 and nu6 interact with Iphi about 500 and 5000 times more strongly than nu4. The paper does not show that these heavier states remain out of equilibrium, and without that the claimed 3+1 cosmology is not established.
[II.C, Eq. (21) and III] The statement that lepton number must be violated at M < 1e-8 eV is presented as a new output, but it is a direct restatement of the input condition M_Iphi < 0.1 eV adopted from Refs. [11,12]. Since M is fixed by that external requirement, the conclusions in Section III that this is a 'very original result' and a 'change of paradigm' should be rephrased as a consistency condition of the scenario rather than an independent prediction.

minor comments (5)

[Eq. (14)] The entry '8, 6 x 10^-3' should read '8.6 x 10^-3'.
[Eqs. (11) and (13)] The notation is inconsistent: Eq. (11) uses v2, Eq. (13) uses vD for the same VEV, and the text earlier considers v2 = 10^2 eV before the benchmark sets vD = 10 eV. The value actually used should be stated consistently and its consequences checked.
[Eq. (15)] The mixing matrix entry '044' presumably should be '0.44', and the fourth-column mixing elements U_e4 and U_mu4 appear approximately a factor of two smaller than what a leading-order evaluation of Eq. (12) with Eq. (13) gives; the numerical diagonalization should be checked and documented.
[Abstract and Introduction] There are several grammatical slips, for example 'claiming have observed' and 'reconciliates', and 'CBM' should be 'CMB'.
[II.D, Eq. (23)] The assumed VEV and parameter hierarchy f > vsigma > v1 >> vphi >> v2 >> M is stated without a demonstration that the full scalar potential has a stable global minimum realizing this ordering; a boundedness and stability check would strengthen the scalar-sector discussion.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the model uses openly chosen benchmark parameters and external cosmological constraints as inputs, not disguised predictions.

full rationale

The paper's central construction is an explicit model-building exercise rather than a derivation of a prediction from first principles. The Yukawa couplings in Eq. (13) are openly labeled 'illustrative benchmark points,' and the masses in Eq. (14) are obtained by direct diagonalization of the mass matrix; this is a parameter demonstration, not a fitted-input-called-prediction, because the paper does not claim to have derived the parameters from independent data. The sub-eV pseudo-scalar condition M_Iφ < 0.1 eV is adopted from the external references [11,12], which are not the author's own prior work, and is then used via Eq. (21) to constrain the lepton-number-violating parameter M; imposing a phenomenological constraint and algebraically converting it into a bound on a Lagrangian parameter is normal model building and does not amount to a circular derivation. The cosmological mechanism itself is cited rather than recomputed, but citation of external results is not circular in the sense used here. The only self-citation, Ref. [23] for Higgs inflation with ξ < 1, is a side remark and is not load-bearing for the neutrino-mass or secret-interaction claims. The numerical failure of the benchmark noted in the skeptical reading would be a correctness defect, not circularity.

Assumptions & free parameters 8 free parameters · 4 assumptions · 4 invented entities

The model's central claims rest on many chosen numbers: six YD entries, three YS entries, the VEVs v2, vphi, the trilinear M, plus the unconstrained quartic couplings. The cosmological viability additionally imports the secret-interaction mechanism of Refs. [11,12] as an assumption. This is a high parameter-count construction with no independent predictive constraint derived in the paper.

free parameters (8)

v2 (vD) = 10 eV
VEV of the second Higgs doublet; sets the Dirac mass scale and is chosen phenomenologically so that v2^2/vphi yields sub-eV active neutrino masses.
vphi = 10^5 eV
VEV of the scalar singlet phi; sets the sterile Majorana masses through YS vphi.
YD matrix entries = YD11=0.018, YD22=-1.3013, YD33=0.3639, YD12=-0.0113, YD13=-0.0383, YD23=-0.7631
Chosen to fit active and sterile neutrino mixings and masses; no symmetry or derivation fixes them.
YS diagonal entries = YS11=2e-5, YS22=0.01, YS33=0.1
Choose the sterile masses (1.4 eV, 0.7 keV, 7 keV) and set the secret coupling g_s=YS11=2e-5 for the eV sterile.
M (LNV trilinear) = M < 4.4e-8 eV
Chosen so that m_Iphi=(9/4)M vphi < 0.1 eV, the condition imported from Refs. [11,12].
f = not fixed; f vsigma >= 36e6 GeV^2 from mu -> e gamma
Trilinear coupling involving sigma; constrained by charged scalar mass and rare decay bound, not otherwise determined.
vsigma (VEV of sigma) = not fixed; satisfies hierarchy f > vsigma > v1
Sets the mass of R2 and the inflaton scale; free parameter.
Quartic couplings lambda_i = unspecified
Free parameters of the scalar potential; required for stability and masses but not numerically evaluated.

assumptions (4)

standard math Type I seesaw block diagonalization, valid when MR >> MD, gives Mlight = -MD^T MR^{-1} MD and Mheavy = MR.
Used directly in Eq. (11); standard and not in question.
domain assumption A sub-eV pseudo-scalar with Yukawa coupling gs in 10^-6 to 10^-5 to sterile neutrinos suppresses their production in the early universe and reconciles eV sterile neutrinos with BBN, CMB and LSS data.
Adopted from Refs. [11,12]; the paper does not recalculate the effect for this model.
ad hoc to paper The scalar potential has a minimum with the VEV ordering v1 >> vphi >> v2 >> M and f > vsigma > v1; the potential is bounded from below and the discrete Z3 x Z2 symmetry is unbroken in a way that preserves the Yukawa structure.
The hierarchy and symmetry are imposed, with no stability or naturalness analysis.
domain assumption The standard cosmological data (BBN, CMB, LSS) indeed disfavor eV sterile neutrinos in the absence of new interactions.
Cites Refs. [5-7]; standard consensus but a background assumption.

invented entities (4)

Three right-handed singlet neutrinos nu_Ri
purpose: Provide Dirac and Majorana masses via low-scale type I seesaw; the lightest (nu4, mass ~1.4 eV) addresses SBL anomalies and nu6 (7 keV) is warm dark matter.
Motivated by SBL anomalies but not directly observed; masses and mixings are fit to data.
Second Higgs doublet H2
purpose: Gives Dirac masses to neutrinos through its eV-scale VEV while the Z2 forbids standard Higgs coupling to neutrinos.
No direct evidence; introduced for the neutrino mass structure.
Scalar singlet phi and its CP-odd component Iphi
purpose: phi gives sterile Majorana masses; Iphi is the sub-eV pseudo-scalar mediator of secret interactions with sterile neutrinos.
The pseudo-scalar mass M_Iphi < 0.1 eV and coupling 2e-5 are chosen to match the secret-interaction mechanism of Refs. [11,12]; no independent signal predicted.
Scalar singlet sigma
purpose: Raises the mass of R2 and may act as the inflaton in Higgs inflation with xi < 1.
Added for scalar-sector structure; no independent evidence.

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Cite this review

Pith. "Pith review of A cosmologically viable eV sterile neutrino model." pith.science (2026). https://pith.science/paper/UXVHI2TZ

@misc{pith2026190809313,
  author       = {Pith},
  title        = {Pith review of: A cosmologically viable eV sterile neutrino model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UXVHI2TZ}},
  note         = {Machine review of arXiv:1908.09313}
}

abstract

The MiniBooNE collaboration recently released a report claiming have observed an excess of electron and anti-electron neutrino with significance of $4.8 \, \sigma$ C.L. corroborating, in this way, the long-standing LSND anomaly. Combined LSND and MiniBooNE analysis reach a significance of $6.0\, \sigma$ C.L. Such a result, if confirmed by future experiments, will cause considerable impact on particle physics since that such anomalies, when interpreted in terms of neutrino oscillation, require the existence of at least one light sterile neutrino. It happens that, on according to standard scenarios, such light sterile neutrino is incompatible with current cosmological data. In this way, understand these anomalies require an extension of the standard model capable of generating tiny masses for both active and sterile neutrinos and re-conciliates such a result with cosmology. An interesting proposal in this direction involve the existence of a secret sector interacting exclusively with sterile neutrinos. In this work we implement the canonical seesaw mechanism into the standard model in such a way that generates tiny masses to the active and sterile neutrinos and embody a secret sector capable of re-conciliating eV sterile neutrinos with cosmology. As other gains, the scalar content required by the implementation of the mechanism provides contribution to rare lepton decays, may accommodate the $g-2$ of the muon and poses a scalar singlet that may drive inflation through Higgs inflation mechanism without problem with loss of unitarity.

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

83 0 . 54 −0. 12 0 . 045 ∼ 10− 5 ∼ 10− 6 −0. 25 0 . 59 0 . 72 −0. 030 −6 × 10− 3 ∼ 10− 5 044 −0. 6 0 . 69 −0. 09 ∼ 10− 4 ∼ 10− 5 −0. 045 0 . 03 0 . 09 1 0 0 ∼ 10− 6 ∼ 10− 4 ∼ 10− 4 0 1 ∼ 0 ∼ 10− 6 ∼ 10− 5 − ∼ 10− 4 0 0 1              . (15) See that the ﬁrst 3 × 3 block recovers the PMNS mixing matrix. Moreover, this mixing matrix says that t...

work page

[2] [2]

= 0 , µ 2 4 − 1 2 (−λ 4V 2 σ + λ 11v2 2 + λ 9v2

work page

[3] [3]

(18) With this in hand, our next step is to obtain the mass matrices of the s calars

− f v2v1 2vσ = 0. (18) With this in hand, our next step is to obtain the mass matrices of the s calars. Firstly, let us obtain the mass matrix of the pseudo-scalars. Taking as basis ( I1 , I 2 , I φ , I σ ), the potential above provides the following mass matrix for the pseudo-scalars of the model M 2 I =        (f vσ +2λ 7v1v2)v2 4v1 − 1 4 (f vσ +...

work page

[4] [4]

(22) For the values of mν6 and Ue6 given above, we obtain τν6 ∼ 1028s

8 × 1021s U 2 e6( mν6 keV)5. (22) For the values of mν6 and Ue6 given above, we obtain τν6 ∼ 1028s. This lifetime is many order longer than the age of the universe. The condition for alleviating the tension among eV sterile neutrino and LSS of the uni- verse is that the pseudo scalar Iφ interact with the dark matter[12]. This is realized in our model sinc...

work page

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Aguilar-Arevalo, et al

A. Aguilar-Arevalo, et al. , Phys. Rev. D 64 (2001) 112007

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